which is a vector in the color space of the external gluons.
The 1-loop virtual amplitudes were computed in refs. [1]}, [2]}, [3]}.
For representing color structures of multi-gluon scattering amplitudes,
like eq. (REF ), it is most convenient to perform a color decomposition
using the choice of basis of refs. [4]}, [5]}, [6]}, [7]}, [8]}.
It is well known that tree-level QCD amplitudes with n external gluons can be decomposed
into color-ordered partial amplitudes, multiplied by associated single color traces
(over all noncylic permutations of fundamental color generators).
Decomposition of color structures of one-loop QCD amplitudes can be done in a similar
way but with an extended color basis including products of two
color tracesThis can be easily understood by combing the statement about tree-level color decomposition
and the Fierz identities of SU(N) color algebra..
